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A coin is made by starting with an equilateral triangle ABC of side 2cm. With centre A an arc of a circle is drawn joining B to C. Similar arcs join C to A and B. Find the area of the coin.

I assumed the method would be to find the combined areas of the curved outer segments, then add the area of the equilateral triangle.

If the area of one of these outer segments is , then the combined area is . The triangle ABC is equilateral, so . , so plugging these numbers into the above equation gives me an area of . The area of the equilateral triangle is , so the total area of the face of the coin should be .

This is apparantly the wrong answer, and I don't see how I've gone wrong. Help appreciated.

Could anyone reccomend any software or websites to draw geometric diagrams? I'm using paint, and doing an awful job, as anyone can see.
The way I did it was treat the triangle and one of the curved outer segments as a sector from a circle with radius 2. To find the area of this, I used . Using 2 as the radius, and as , we get an answer of .
Take away the area of the triangle to just get the area of the curved outer segment. Multiply this by 3 (there are 3 segments), then add the area of the triangle back on to get the whole area
Last edited by CharlieBoardman; 03-07-2012 at 12:37.
(Original post by CharlieBoardman)
The way I did it was treat the triangle and one of the curved outer segments as a sector from a circle with radius 2. To find the area of this, I used . Using 2 as the radius, and as , we get an answer of .
Take away the area of the triangle to just get the area of the curved outer segment. Multiply this by 3 (there are 3 segments), then add the area of the triangle back on to get the whole area
Thanks, using your method, I get the final answer as , but according to the textbook the correct answer is . I can't see where I've gone wrong, can you?
(Original post by Julii92)
Thanks, using your method, I get the final answer as , but according to the textbook the correct answer is . I can't see where I've gone wrong, can you?
Hmm. I actually get the answer of .

EDIT: I see where I have gone wrong. Stupid mistake. The area of the triangle isn't 2. Give me a minute.
Last edited by CharlieBoardman; 03-07-2012 at 13:48.
(Original post by CharlieBoardman)
Hmm. I actually get the answer of .

I think now you're making the same mistake I did which is to assume that the area of the equilateral trianlge is , when it is actually
(Original post by Julii92)
I think now you're making the same mistake I did which is to assume that the area of the equilateral trianlge is , when it is actually
Yes school boy error! I get the same answer as you. I am assuming that the book is incorrect - unless we have made another error.
Last edited by CharlieBoardman; 03-07-2012 at 13:57.
(Original post by CharlieBoardman)
Yes school boy error! I get the same answer as you. I am assuming that the book is incorrect - unless we have made another error.
I hope you're right!